What the title says. I am sure it had something to do with the card design text, which means creatures should not be stolen in the first place.
Refuse/Cooperate sometimes grabs supports as well. It seems like it’s more likely to happen if your opponent doesn’t have any spells left in their graveyard.
But supports will stay on the board if you steal them with Cooperate.
Yes supports work perfectly when stolen, I just felt it might be helpful info, especially the no spells left in your opponent’s graveyard for reproduction purposes.
P.S. The support stealing came in real handy when I got imminent doom from Nicol Bolas. 
Oh yes, it’s helpful info. I’m just adding on to what you said.
This also happens when the opponent uses Cooperate as well.